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SUMMARY:Spectral estimates\, heat observability\, and thickness on Riemann
 ian manifolds.
DTSTART:20250929T120000Z
DTEND:20250929T130000Z
DTSTAMP:20260518T152300Z
UID:indico-event-14521@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alix Deleporte (LMO - Université Paris Saclay)\n\nE
 igenfunctions of the Laplacian cannot vanish on a set of positive measure.
  Quantitative versions of thisunique continuation are well-known on fixed 
 Riemannian manifolds : the L2 norm of an eigenfunction isbounded by its L2
  norm on a set of positive measure times a constant which grows exponentia
 lly with the frequency. This growing rate is sharp and reflects in observa
 bility properties for the heat equation.\nIn this talk\, I will present re
 cent results\, in collaboration with M. Rouveyrol (Uni. Bielefeld) about t
 hese questions in a non-compact setting\, and/or uniformly with respect to
  the metric. Quantitative unique continuation\, and observability of the h
 eat equation\, hold under a necessary and sufficient condition of thicknes
 s of the observed set : it must intersect every large enough metric ball w
 ith a mass bounded from below\, proportionally to the mass of the ball its
 elf. \nI will talk about the case of non-compact hyperbolic surfaces\, th
 en about much more general Riemannian manifolds (in progress!). The proof 
 crucially uses the Logunov-Mallinikova estimates.\n\nhttps://indico.math.c
 nrs.fr/event/14521/
LOCATION:Amphi Schwartz
URL:https://indico.math.cnrs.fr/event/14521/
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